Stable bi-frequency spinor modes as Dark Matter candidates

TL;DR

This paper demonstrates that bi-frequency spinor solitary waves in certain scalar self-interacting systems are generally stable and could potentially serve as dark matter candidates, expanding understanding of their stability and physical relevance.

Contribution

It introduces the existence and stability analysis of bi-frequency solitary waves in spinor systems with scalar self-interaction, highlighting their potential as dark matter candidates.

Findings

Bi-frequency modes are generically stable in these systems.

Only bi-frequency modes can be dynamically stable.

Stable bi-frequency modes may serve as dark matter storages.

Abstract

We show that spinor systems with scalar self-interaction, such as the Dirac--Klein--Gordon system with Yukawa coupling or the Soler model, generically have bi-frequency solitary wave solutions. We develop the approach to stability properties of such waves and use the radial reduction to show that indeed the (linear) stability is available for a wide range of parameters. We show that only bi-frequency modes can be dynamically stable and suggest that stable bi-frequency modes can serve as storages of the Dark Matter. The approach is based on linear stability results of one-frequency solitary waves in (3+1)D Soler model, which we obtain as a by-product.